$\begin{array}{l}\phantom{\phantom{;}2x^{2}+3x\phantom{;}-1;}{\phantom{;}4x\phantom{;}-5\phantom{;}\phantom{;}}\\\phantom{;}2x^{2}+3x\phantom{;}-1\overline{\smash{)}\phantom{;}8x^{3}+2x^{2}-3x\phantom{;}+8\phantom{;}\phantom{;}}\\\phantom{\phantom{;}2x^{2}+3x\phantom{;}-1;}\underline{-8x^{3}-12x^{2}+4x\phantom{;}\phantom{-;x^n}}\\\phantom{-8x^{3}-12x^{2}+4x\phantom{;};}-10x^{2}+x\phantom{;}+8\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x^{2}+3x\phantom{;}-1-;x^n;}\underline{\phantom{;}10x^{2}+15x\phantom{;}-5\phantom{;}\phantom{;}}\\\phantom{;\phantom{;}10x^{2}+15x\phantom{;}-5\phantom{;}\phantom{;}-;x^n;}\phantom{;}16x\phantom{;}+3\phantom{;}\phantom{;}\\\end{array}$

$4x-5+\frac{16x+3}{2x^2+3x-1}$